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An essay on proof, conviction, and explanation: multiple representation systems in combinatorics
- Source :
- Educational Studies in Mathematics. 103:173-189
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- There is a longstanding conversation in the mathematics education literature about proofs that explain versus proofs that only convince. In this essay, we offer a characterization of explanatory proofs with three goals in mind. We first propose a theory of explanatory proofs for mathematics education in terms of representation systems. Then, we illustrate these ideas in terms of combinatorial proofs, focusing on binomial identities. Finally, we leverage our theory to explain audience-dependent and audience-invariant aspects of explanatory proof. Throughout, we use the context of combinatorics to emphasize points and to offer examples of proofs that can be explanatory or only convincing, depending on how one understands the claim being made.
- Subjects :
- Mathematical logic
Computer science
General Mathematics
media_common.quotation_subject
05 social sciences
050301 education
Combinatorial proof
Context (language use)
Representation (arts)
Mathematical proof
Education
Combinatorics
Proof theory
0501 psychology and cognitive sciences
Conversation
0503 education
Binomial coefficient
050104 developmental & child psychology
media_common
Subjects
Details
- ISSN :
- 15730816 and 00131954
- Volume :
- 103
- Database :
- OpenAIRE
- Journal :
- Educational Studies in Mathematics
- Accession number :
- edsair.doi...........f59956d4b4c7d25f2f66646e9af5988e